Build your own brain

Rules and Mechanics:

1. Neurons: 
   • Neurons are represented as circles on the canvas.
   • They can be added randomly or with a brush tool.
   • Neurons have a position, potential, and can form connections with other neurons.

1. Connections: 
   • Connections between neurons are represented as lines.
   • They form based on proximity and activity of neurons.
   • Connections have a "strength" represented by their last used time.

1. Stimulation: 
   • Neurons can be stimulated manually or automatically.
   • When stimulated, a neuron's potential increases.

1. Firing: 
   • If a neuron's potential exceeds the threshold, it fires.
   • Firing resets the neuron's potential and triggers a refractory period.

1. Movement: 
   • Neurons can move around the canvas.
   • Movement speed depends on the number of connections.

How Neurons Work in This Simulation:

1. Potential: Each neuron has a potential value that increases when stimulated.
2. Threshold: If the potential exceeds a certain threshold, the neuron fires.
3. Firing: When a neuron fires, it: 
   • Resets its potential to 0
   • Enters a refractory period
   • Stimulates connected neurons
   • May form new connections

1. Connections: Neurons can form connections with nearby neurons when they fire simultaneously or when one is firing and the other has high potential.
2. Plasticity: Connections have a "time limit" (plasticity). If not used frequently, they disappear.

Hebbian Theory in the Simulation:

Hebbian theory is summarized by the phrase "Neurons that fire together, wire together." This simulation implements a simplified version of this principle:

1. Connection Formation: When two neurons fire simultaneously or when one fires while the other has high potential, they form a connection. This mirrors the Hebbian principle of strengthening connections between co-active neurons.
2. Connection Strength: Each time a connection is used (when a firing neuron stimulates another through that connection), its "last used" time is updated. This represents the strengthening of frequently used connections.
3. Connection Pruning: Connections that haven't been used recently (beyond the plasticity time limit) are removed. This represents the weakening and eventual loss of unused connections, a key aspect of neural plasticity.
4. Spatial Component: Connections can only form between neurons within a certain distance, representing the spatial limitations in real neural networks.
5. Activity-Dependent Plasticity: The simulation includes both the formation of new connections and the pruning of unused ones, reflecting the dynamic, activity-dependent nature of neural plasticity described by Hebbian theory.

This simulation provides a simplified but interactive model of neural network dynamics, incorporating key elements of Hebbian learning. Users can observe how patterns of activity lead to the formation and strengthening of connections, while inactivity leads to their weakening and removal. The various controls allow users to experiment with different parameters and observe their effects on the network's behavior and structure.